1. Revision Description Reflect and Review Teasers Recall basics of geometrical shapes.

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1 1. Revision Description Reflect and Review Teasers Recall basics of geometrical shapes. A book, a birthday cap and a dice are some examples of 3-D shapes. 1) Write two examples of 2-D shapes and 3-D shapes from your day-to-day life. 2. Comparing the Lengths of Line Segments Description The lengths of line segments can be compared by observation. But this method is not applicable in all situations. Comparing can also be done by tracing, i.e., we take a tracing paper and make the replica of one line segment and keep this traced sheet on the second line segment and then find out which is longer. But this is time consuming. Comparing lengths of line segments can be done by using ruler. We place one end of the first line segment at 0 mark of the ruler and find the position where the other end of the segment is with respect to the ruler. Similarly we find the length of other line segments and compare. The best way of comparing the lengths of two line segments is using a divider. We open the divider in such a way that the two tips of the divider coincide with the two ends of a line segment. Now without disturbing the opening of the divider, we place it in such a way that the tip of one of its arm coincides with one end of second segment and then check whether the tip of the other arm coincides with the other end or not. Reflect and Review See below the Teasers See below the Answers 1) Length of < Length of < Length of. 1

2 Reflect and Review: B D A C Here, line segment AB is smaller than segment CD on observation. Teasers: 1) Compare the lengths of the line segments PQ, QR and RS from the below figure. P Q R S m 3. Collinear and Non-collinear Points Description See below the Reflect and Review See below the Teasers See below the Answers 1) Y is the midpoint of. If three or more points are lying on the same line then they are called collinear points and the points which do not lie on the same line are called non-collinear points. Reflect and Review: A B C D l Here, points A, B, C and D are collinear. Teasers: 1) Find which points in the following figure are mid-points of the other two. X Y Z W t 2

3 4. Parallel and Perpendicular lines; Concurrent lines Description Reflect and Review Teasers See below the The altitudes of a triangle are concurrent, since they intersect at the orthocentre. 1) Give some examples of concurrent lies that you know. If two lines m and n never intersect each other and the distance between them is the same always, then they are said to be parallel to each other, and it is represented as m n. m If two lines m and n intersect each other at a point O making a right angle, then they are said to be perpendicular to each other, and it is represented as m n. n O m n If three or more lines pass through the same point, then they are called concurrent lines. l q p n m 3

4 5. Angles Right, Straight and Complete Description Reflect and Review Teasers Answers See below 1) Where will the hand of a 1) At 12 the clock stop, if it starts at 4 o clock If the hour s hand of a clock turns (clockwise) from 2 to 5, it moves one right angle. and makes of a revolution? 2) Which direction will you face if you are initially facing East and then make ¼ of a revolution clockwise? 2) South 1) Taking a left turn (Anti-clockwise) or right turn (Clockwise) from the present position is said to be turning about right angle. 2) Turning two right angles in the same direction is said to be making a straight angle. 3) Turning four right angles in the same direction or turning two straight angles in the same direction makes a full turn. One complete turn is called one revolution. The angle turned to make one revolution is called a complete angle. 4) When the hand of a clock turns from one point and returns to the same position, it completes one revolution. N W E Right Angle i.e., one right turn Anti-clock wise S Clock wise Straight angle i.e., two right turns Three right turns 4

5 6. Angles Acute, Obtuse, Reflex Description See below the Reflect and Review Angle measuring is said to be an obtuse angle, since it is more than 90 0 and less than Teasers 1) Pick out the acute, obtuse, reflex, right, straight and complete angles from the following: 90 0, 89 0, 180 0, 360 0, 261 0, 112 0, 68 0, 345 0, 137 0, Answers 1) Acute angles: 89 0 and 68 0 Right angles: 90 0 Obtuse angles: 112 0, Straight angles: Reflex angles: 261 0, 270 0, Complete angles: An angle whose measure is less than a right angle is called an acute angle. An angle whose measure is more than a right angle but less than a straight angle is called an obtuse angle. A reflex angle is larger than a straight angle. Measuring angles: To measure an angle we need a tool or an instrument called Protractor. It is divided into 180 equal parts, each part measures one degree denoted as 1. The marking starts from 0 on the right side and ends with 180 on the left side and vice versa. To measure an angle using a Protractor 5

6 1) Place the protractor in such a way that the midpoint of the straight edge of the protractor coincides with point B. 2) Adjust the position of the protractor so that the straight edge coincides with the arm BC of angle ABC. 3) There are two scales on the protractor. We should consider the scale whose 0 -mark coincides with the horizontal straight edge. 4) The mark shown by AB on the curved edge gives the measure of the angles. Here it is 60. So, ABC = Triangles Description Reflect and Review Teasers Answers See below the A triangle with sides 5 cm, 5 cm and 6 cm is said to be an isosceles triangle, since it has two of its sides equal. A triangle with angles 35 0, 55 0 and 90 0 is said to be a right angled triangle, since one of its angles is ) Name the triangle with angles 45 0, 45 0, ) Can any triangle have one right angle and one obtuse angle? 1) Rightangled and isosceles triangle 2) No. A polygon which has three sides is called a triangle. Types of triangles based on sides A triangle having all three sides unequal is called a scalene triangle. A triangle having two equal sides is called an isosceles triangle. A triangle having all three sides equal is called an equilateral triangle. 6

7 Types of triangles based on angles If all the angles of a triangle are less than 90 0, then it is called an acute-angled triangle. If one angle of a triangle is a right angle, then it is called a right-angled triangle. If one angle of a triangle is obtuse, then it is called an obtuse-angled triangle. 8. Quadrilaterals Description Reflect and Review Teasers Answers See below 1) Square the A square is said to be a regular polygon, since each of its angle is 90 0 and all sides are equal. 1) Name the quadrilateral which satisfies the properties of both rectangle and rhombus. 2) Name a trapezium whose non-parallel sides are equal. 2) Isosceles trapezium A four-sided polygon is called a quadrilateral. It has four sides, four angles and two diagonals. There are different types of quadrilaterals and special quadrilaterals have different properties based on their sides, angles and diagonals. A quadrilateral in which One pair of opposite sides are parallel is called a trapezium. Both the pairs of opposite sides are parallel is called a parallelogram. All the sides are equal is called a rhombus Both the pairs of opposite sides are parallel and each angle is 90 0 is called a rectangle. All sides are equal and each angle is 90 0 is called a square. In which two pairs of adjacent sides are equal is called a kite. Trapezium Parallelogram Rhombus Rectangle Square Kite 7

8 9. Polygons Description See below the Reflect and Review A polygon which has no diagonal is a triangle, since no vertex of a triangle have an opposite vertex, it has only an opposite side. Teasers Name the polygons given below. 1) Answers 1) Irregular hexagon 2) Irregular decagon 2) A closed rectilinear figure with three or more sides is called a polygon. A polygon in which all the sides are equal and all the angles are equal is called a regular polygon. 8

9 10. Three-dimensional (3-D) Shapes Description Reflect and Review Teasers Answers See below the 1) Cylinder 2) Cone. A prism with circle bases is called a cylinder. Since, all its other faces become one curved surface. 1) Name a three-dimensional shape that has no vertices and edges. 2) Name the prism in which the base of a prism is a circle and its surrounding triangular faces are all curved as one face. Shapes having length, breadth and height are called three-dimensional shapes. Cuboid, cube, prism, pyramid, cylinder, cone, sphere are some of the three-dimension shapes that we come across in our day-today life. The flat surfaces are called the faces of a solid shape. Two faces meet at a line segment. This line segment is called an edge of the solid. Three edges meet at a point. The point of intersection of the edges is called the vertex of the solid. A prism has two identical bases and all its other faces are rectangles. A pyramid has triangular surfaces around and bases are different polygons. 9

10 Cuboid Cube Cylinder Cone Sphere Prism Pyramid 10